What is the first derivative of y/x ?

The first derivative of y/x is 1/x

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derivative of y/x

derivative of

\frac{y}{x}

\frac{1}{x}

Solution steps

\frac{d}{d y} (\frac{y}{x})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{x} \frac{d y}{d y}

Apply the common derivative:

\frac{d y}{d y} = 1

= \frac{1}{x} \cdot 1

Simplify

= \frac{1}{x}

(\frac{100}{lo g _{10} ( 2 x + 1 )})^{^{'}}

f (x) = x^{3} e^{2 x}

x \to 1 lim (x^{\frac{3}{1 - x}})

y^{^{''}} - 5 y^{^{'}} - 6 y = 0, y (0) = 5, y^{^{'}} (0) = 12

\int \frac{1}{10 x ^{\frac{1}{2}} - x} d x